The only thing I enjoy about Nassau is Atlantis and even that isnt the best (weve stayed there several times). Jamaica would be #1 on my hit list. Its dirty, and Ive never felt safe there, even when walking with a group. We now stay on the ship if we docked there.
I used to love Grand Cayman, but it has just exploded since we stayed there in the early 90's, losing its small island appeal. I hadnt been back until '03 and was shocked by the development. You used to be able to drive along 7 mile beach and actually see the water. Not anymore. It was impossible to get around the stores and island with 7+ ships in port that day (3-4 were the biggies, including ours the Navigator). While I will still go ashore there, its not as appealing as it used to be.